## Engineering Mechanics - Dec 2014

### First Year Engineering (Semester 2)

TOTAL MARKS:

TOTAL TIME: HOURS

**1** Give the static equilibrium equations.(2 marks)
**10** Define instantaneous center of rotation.(2 marks)

### Solve any one answer from Q11 (a) & Q11 (b)

**11 (a)** Four forces act on bolt A as shown. Determine the resultant of the forces on the bolt shown in fig. 11(a)

(16 marks)
**11 (b)** Consider the 75kg crate shown in the space diagram of fig. Q11 (b). This crate was lying between two buildings, and it is now being lifted on a truck, which will remove it. The crate is supported by a vertical cable, which is joined at A to two ropes which pass over pulleys attached to the buildings at B and C. It is desired to determine the tension in each of the ropes AB and C.

(16 marks)

### Solve any one answer from Q12 (a) Q12 (b)

**12 (a)** Determine the magnitude and direction of the smallest force F, shown in Fig. Q12(a) which will maintain the packages shown in equilibrium. Note that the force exerted by the package is perpendicular to the incline.

(16 marks)
**12 (b)** A 20-g ladder Fig. Q.12(b) used to reach high shelves in a store room is supported by two flanged wheels A and B mounted on rail and by an unflanged wheel C resting against a rail fixed to the wall. An 80-kg man stands on the ladder and leans to the right. The line of action of the combined weight W of the man and ladder intersects the floor at point D. Determine the reactions at A, B and C.

(16 marks)

### Solve any one answer from Q13 (a) & Q13 (b)

**13 (a)** Determine the moment of inertia of the shaded area as shown in Fig. Q.13(a) with respect to the axis.

(16 marks)
**13 (b)** For the section in Fig. Q13(b), the moments of inertia with respects to the x and y axes have been computed and are known to be _{x}=10.38 mm^{4} I_{y}=6.97 mm^{4}. Determine:

i) The orientation of the principal axes of the section about O.

ii) The value of the principal moments of inertia of the section about O.

(16 marks)

### Solve any one answer from Q14(a) & Q14 (b)

**14 (a)** The two blocks in Fig. Q.14(a) start from rest. The horizontal plane and the pulley are frictionless, and the pulley is assumed to be of negligible mass. Determine the acceleration of each block and the tension in each cord.

(16 marks)
**14 (b)** Two blocks are joined by an inextensible cable as shown in Fig. Q.14(b). In the system is released from rest, determine the velocity of block. A after it has moved 2m. Assume that the coefficient of kinetic friction between block A and the plane is ?_{k}=0.25 and that the pulley is weightless and frictionless.

(16 marks)

### Solve any one answer from Q15(a) & Q15 (b)

**15 (a)** A support block is acted upon by two forces as shown in Fig. Q.15(a). Knowing that the coefficient of friction between the block and the incline are ?_{s}=0.35 and ?_{k}=0.25, determine the force P required

i) To start and block moving up the incline

ii) To keep it moving up,

iii) To prevent it from sliding down.

(16 marks)
**15 (b)** A cord is wrapped around the inner drum of a wheel and pulled horizontally with a force 200N as figure Q.15(b). The wheel has a mass of 50 kg and a radius of gyration of 70 mm. Knowing that ?_{s}=0.20 and ?_{k}=0.15, determine the acceleration of G and the angular acceleration of the wheel.

(16 marks)
**2** Define Lami's theorem.(2 marks)
**3** Define couple.(2 marks)
**4** State Varignon's theorem(2 marks)
**5** State parallel axis theorem(2 marks)
**6** Define principle moments of inertia(2 marks)
**7** Define Newton's law (second law) of motion.(2 marks)
**8** Give the equation of work energy for a rectilinear motion.(2 marks)
**9** Define limiting friction.(2 marks)